How to Import a finished 3D model with texture into a new blender file?
For most things, there are multiple ways to complete them in Blender, and importing a material is one of them. The procedure outlined by Zac Perry in his answer above certainly works, but if you are wanting to append just a material, an alternate method is to do steps 1 through 4 as Zac outlines them in his answer, but in step 5, instead of going to the object folder, and appending the object, you can go to the material folder, and append the material. 

In the same manner, if you wanted just to append a texture from one file to another, and assign it in the new file to a different material, you can do that by navigating to the texture folder, and appending it from there.

Both of these (and for that matter, appending an object as suggested by Zac) become orders of magntitude easier if one takes the time to give meaningful names to objects, materials, and textures, and for that matter, to meshes, too.